A quadratic approach to allometry yields promising results for the study of growth

Abstract

Julian HUXLEY (1924) came to the conclusion that intra-specific growth usually follows a sequence of power curves. So HUXLEY claimed that during growth sudden changes in the growth rate can occur. The restudy of his material, however, reveals that his observations closely follow single quadratic curves. As a result the intra-specific allometry studied by HUXLEY is comparable to ontogenetic allometry. The quadratic factor of the quadratic equations obtained, represents the growth rate; it shows the constant increase (positive factor) or decrease (minus factor) of one of the measurements for a constant increase in the other measurement with which it is compared. The quadratic factor explains the entire growth process and is the same for the smaller (younger) and larger (older) specimens. It could probably permit the prediction of the shape of larger and/or smaller animals not yet found, or give a clue to some evolutionary changes. By using the quadratic parabola there is no need to postulate "sudden changes in the growth curve" and so it appears that HUXLEY's power curve can be abandoned.